The energy of the $K_\alpha$ $X$-ray line of an element is $8578$ units,and the energy of the $L$ level is $-2859$ units. The energy of the $K$ level is . . . . . . units.

In an $X$-ray tube, electrons emitted from a filament (cathode) carrying current $I$ hit a target (anode) at a distance $d$ from the cathode. The target is kept at a potential $V$ higher than the cathode, resulting in the emission of continuous and characteristic $X$-rays. If the filament current $I$ is decreased to $I/2$, the potential difference $V$ is increased to $2V$, and the separation distance $d$ is reduced to $d/2$, then:
$(A)$ The cut-off wavelength will reduce to half, and the wavelengths of the characteristic $X$-rays will remain the same.
$(B)$ The cut-off wavelength as well as the wavelengths of the characteristic $X$-rays will remain the same.
$(C)$ The cut-off wavelength will reduce to half, and the intensities of all the $X$-rays will decrease.
$(D)$ The cut-off wavelength will become two times larger, and the intensity of all the $X$-rays will decrease.

$X-$rays are in nature similar to

If $\lambda_{Cu}$ is the wavelength of the $K_{\alpha}$ $X$-ray line of copper (atomic number $Z = 29$) and $\lambda_{Mo}$ is the wavelength of the $K_{\alpha}$ $X$-ray line of molybdenum (atomic number $Z = 42$),then the ratio $\frac{\lambda_{Cu}}{\lambda_{Mo}}$ is close to:

The largest distance between the interatomic planes of a crystal is $10^{-7} \text{ cm}$. The upper limit for the wavelength of $X$-rays which can be usefully studied with this crystal is ............ $\mathring{A}$.

Atomic number of anticathode material in an $X$-ray tube is $41$. Wavelength of $K_\alpha$ $X$-ray produced in the tube is ........ $\mathring A$.